Multiresolution analysis multigrid solver

Nicolas Ray and Bruno Levy and Jean-Claude Paul. ( 2002 )
in: 22th gOcad Meeting, ASGA

Abstract

This paper presents a multi-resolution framework to speed-up existing numerical algorithms for triangulated surfaces. Our solution is based on a new representation of triangulated surfaces, that we will refer to as a Transactional Topologicalal Model (TTM). The TTM makes it possible to efficiently create levels of details of a surface, and efficiently navigate between those levels. Moreover, the surface can be traversed by the standard iterators, whatever the level under consideration, which facilitates adapting the existing algorithms to this new structure. We show how to adapt Hoppe’s Progressive Meshes to this data structure. Our new parameterization method (Least Squares Conformal Maps) and DSI are demonstrated using this representation, which results in dramatic speed improvements for the convergence of the solver.

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    BibTeX Reference

    @inproceedings{RayRM2002,
     abstract = { This paper presents a multi-resolution framework to speed-up existing numerical algorithms for triangulated surfaces. Our solution is based on a new representation of triangulated surfaces, that we will refer to as a Transactional Topologicalal Model (TTM). The TTM makes it possible to efficiently create levels of details of a surface, and efficiently navigate between those levels. Moreover, the surface can be traversed by the standard iterators, whatever the level under consideration, which facilitates adapting the existing algorithms to this new structure. We show how to adapt Hoppe’s Progressive Meshes to this data structure. Our new parameterization method (Least Squares Conformal Maps) and DSI are demonstrated using this representation, which results in dramatic speed improvements for the convergence of the solver. },
     author = { Ray, Nicolas AND Levy, Bruno AND Paul, Jean-Claude },
     booktitle = { 22th gOcad Meeting },
     month = { "june" },
     publisher = { ASGA },
     title = { Multiresolution analysis multigrid solver },
     year = { 2002 }
    }